A group backed by a longtime Hillary Clinton supporter alleged to the Justice Department this week that Republican presidential front-runner Donald Trump illegally promised former rival Ben Carson a position in his administration in exchange for an endorsement.

"It has recently come to light that Mr. Donald Trump may have willfully offered Dr. Ben Carson an appointment to his administration should he become president in return for supporting his candidacy in violation of 18 U.S.C. § 599," the American Democracy Legal Fund said in a letter to the federal agency.

The two-page letter, dated Tuesday, was reported by Politico on Thursday. It was written by Brad Woodhouse, the fund's president, and addressed to Raymond Hulser, who heads the Justice Department's Public Integrity Section.

The American Democracy Legal Fund is bankrolled by David Brock, the founder of Media Matters and longtime Clinton supporter.

"ADLF respectfully requests that you investigate this matter and take all appropriate action as soon as possible," the letter says.

The retired pediatric neurosurgeon talked with Malzberg three days after he endorsed Trump. Carson had quit the race for the GOP nomination on March 4.

According to Woodhouse's letter, Carson was vague when Malzberg asked about what he and Trump might have discussed before the endorsement.

Carson only said that Trump told him that he would "surround himself with very good people."

"I'm not going to reveal any details about it right now, because all of this is still very liquid," Carson told Malzberg.

Two days after that interview, however, the letter alleges that Carson denied that his endorsement was in exchange for any administration post.

He did that in an interview with Bianna Golodryga of Yahoo News, Politico reports.

"That would be ridiculous," Carson said in the interview. "I would never ask for such a thing.

"And people take liberties and then you believe what they say," he added. "That’s just not true."

The supporting material with Woodhouse's letter also includes reports from The Washington Post and CNN on Carson's endorsement, according to Politico.

"Dr. Carson’s comments strongly suggest that Mr. Trump promised him an administration position in return for his endorsement," he said in the letter.

"Dr. Carson's comments indicate that Mr. Trump used the promise of a role in his administration to secure Dr. Carson’s support for his presidential campaign," he added. "For the above-stated reasons, we respectfully request that you undertake an immediate investigation of this matter."

The letter is the fund's second to the Justice Department against Trump questioning campaign matters in the previous nine months, Politico reports.

Representatives for neither Trump nor the Justice Department immediately responded to questions for comment from Politico.

A group backed by a longtime Hillary Clinton supporter alleged to the Justice Department this week that Republican presidential front-runner Donald Trump illegally promised former rival Ben Carson a position in his administration in exchange for an endorsement.